Predicting Time-Dependent Flow Over Complex Geometries Using Operator Networks
This provides a practical tool for engineers and researchers needing rapid flow predictions over complex geometries, though it is incremental with error accumulation in fine-scale wakes.
The paper tackles the challenge of creating fast, geometry-generalizing surrogates for unsteady flow by developing a time-dependent, geometry-aware Deep Operator Network that predicts velocity fields for moderate-Re flows around parametric and non-parametric shapes. The model achieves ~5% relative L2 single-step error and up to 1000X speedups over CFD on held-out shapes.
Fast, geometry-generalizing surrogates for unsteady flow remain challenging. We present a time-dependent, geometry-aware Deep Operator Network that predicts velocity fields for moderate-Re flows around parametric and non-parametric shapes. The model encodes geometry via a signed distance field (SDF) trunk and flow history via a CNN branch, trained on 841 high-fidelity simulations. On held-out shapes, it attains $\sim 5\%$ relative L2 single-step error and up to 1000X speedups over CFD. We provide physics-centric rollout diagnostics, including phase error at probes and divergence norms, to quantify long-horizon fidelity. These reveal accurate near-term transients but error accumulation in fine-scale wakes, most pronounced for sharp-cornered geometries. We analyze failure modes and outline practical mitigations. Code, splits, and scripts are openly released at: https://github.com/baskargroup/TimeDependent-DeepONet to support reproducibility and benchmarking.